The process of fiting some statistical model to a particular set of data. Mostly done on a computer, and using varied numerical methods such as optimization or numerical integration, or simulation.

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Deriving errors for fitted parameters using Monte Carlo

I have the following data: One 2D image, each of its pixels is a measurement. I will call this "data map". One 2D image, each of its pixels is the error (1 sigma) of the above measurements. I will ...
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36 views

Using ARIMA to Create a Model in R

I'm trying to get understand why the values for my model are different when using two different functions. The first one is from Example 9.2 (International Visitors to Australia), using the ...
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10 views

Power Law reweighting the tails [duplicate]

I am trying to show that from two sets of data, one obeys a power law and the other not. I am trying to quantify that using a numerical tool performing a power law. My tool, python-scipy fitting tool, ...
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1answer
82 views

data and curve fitting

I have several datasets that I need to be able to fit (the goal is to find the outliers). The datasets were created by groups of images and the x is an index number of the image and y is a focus ...
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1answer
48 views

Least squares with exponential model

I'm trying to fit values from this model $$y(x)=ae^{−bx}+c$$ where a, b and c are 3 different parameters that I want to find with least squares. So using least squares I want to find the value of a, ...
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2answers
63 views

Fit exponential distribution with noise

I'm trying to fit an exponential with noise (which in this case is a constant $c$) like this one $$ y(x) = \alpha e^{- \alpha x} + c \text{ ,}$$ having $(x_i, y_i)$ values (So $\alpha$ and $c$ are ...
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2answers
413 views

Difference between regression analysis and curve fitting

Can anybody please explain to me the real difference(s) between regression analysis and curve fitting (linear and nonlinear), with an example if possible? It seems that both try to find a ...
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1answer
30 views

How does the covariance matrix of a fit get computed?

I often have to fit data of physical experiments as a student. I always use (python's) functions like numpy.polyfit or scipy.optimize.curve_fit for that purpose. They also allow you to retrieve the ...
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23 views

Fitting measured, real-world data to theoretical distribution: How to test goodness?

I have a large sets of real-world user data (30k, 80k, 90k measurements). To be precise those are simply session lengths for a specific system. I want to create a theoretical model of this, to ...
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4 views

How to Use fitdist to Fit Johnson Familiy of Distributions in R? [migrated]

I would like to fit a a Johnson distribution to some data using the fitdistrplus R package, in order to compare with other distribution fits. The approach I have taken is to use the SuppDists package ...
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1answer
30 views

How can I avoid misidentification of a exponential distribution as Gamma or Weibull?

I'm trying to write a piece of code in R that identifies a set of sample data as belonging to a specific distribution and pull the specific distribution parameters, by performing the K-S test and ...
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39 views

what to do with ridiculous but valid leverage points

So I'm having some difficulty fitting a linear model to the data (see other post here glm model fit - can't find a family/link combination that produces good fit). In particular, I'm worried ...
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1answer
75 views

glm model fit - can't find a family/link combination that produces good fit

I am having difficulty finding a correct glm model to fit my data. The outcome is the length of time in months a person will spend in prison (sentence length). It's technically a count, all positive ...
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2answers
120 views

How to change the null hypothesis of the coefficient in the least squares fitting?

I have a least square fitting like this: fit = lsfit(log10(M), log10(RS), wt) This function lists statistics and p-values for the coefficient considering the ...
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1answer
98 views

Linear models: estimating the b vector on R

Starting from the basic linear model problem: $$ y=Xb+e $$ And the least squares method of $b$ estimation $$ \hat{b}=(X'X)^{-1}X'y $$ And also considering a model not of full rank (an one-way design, ...
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58 views

How to avoid an overfitting?

The standard way to avoid an over-fitting is to use a "validation set". It means that we split the data into two parts. The first part we use to fit (train) and the second part we use to validate. ...
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22 views

Purpose of fitting parallel lines

I'm a student. I have a dataset of a set of observations split across three factors/categories. I'm being asked to fit three regression-lines with identical slope (but different intercepts, ...
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33 views

Fitting an envelope to x-y data in R

I have some data that I'd like to create an envelope for it. As in the picture, the data is always positive and I'm looking for something that will capture my crudely hand drawn red line. It should ...
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17 views

min ChiSquare to fit dipole axis

I am trying to fit a dipole. As I am not sure about some aspects (and not sure whether I understand it at all) I would like to ask this question here. Basically I have a distribution of $n$ sample ...
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22 views

How to fit quantized data

I have some measurements which were quantized during measuring. Now I want to get the overall change during a period of time, e.g. 15 minutes. Because of quantization however, the same value is ...
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15 views

How to divide scattered points among multiple curves? [duplicate]

I have the following scattered points graph: To me, it seems that the points describe 2 (maybe 3) logarithmic curves. Is there a way to say which point belongs to which curve?
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1answer
48 views

Do predicted values differ if variables included stepwise or simultaneously?

You make a linear model #1 of the following form to predict adult human height: $$ y = \beta_{0.1} + \beta_{1.1}\text{Height}_\text{dad} + \beta_{2.1}\text{Height}_\text{mom} $$ You calculate fitted ...
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33 views

choosing between non-linear/logistic regression models

We are fitting regression models to dose-reponse data obtained from drug assays. Where a drug has an effect on cell viability, there is often a sigmoidal relationship between the proportion of viable ...
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10 views

Linear fit parameter-errors as a function of the number of data-points

I am trying to work out the errors of $m$ and $b$ in a linear least-square fit of a straight $y = m \cdot x + b$ to $N$ equally-spaced data points $Y_i$ on the interval $I = [-\Delta x \cdot ...
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28 views

How do I interpret which model is the best fit for my distribution (AIC)?

I'm new here so looking for some guidance; How do I interpret the following variables to understanding which model is considered the best fit to my distribution. ...
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21 views

Fit a transition matrix

Probably I am asking something very simple, but I am unable to figure out the answer from previous posts. I have a set of data with the age (in years) an the condition (in a class form 1 - good to 5 - ...
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1answer
100 views

Finding probability distribution that describes data

I have tried to fit several distributions to my continuous data (Pareto, Log-normal, Exponential, Gamma). The distribution of data is given below. I used Kolmogorov-Smirnov test to compare my data ...
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18 views

Should I still compare my distrbution to others if I've found a fit?

I'm using the ghpy package in R to model some currency data. I currently comparing fits with the lik.ratio.test with the ...
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10 views

How do I evaluate if an SIR model is consistent with a new-product diffusion model?

Background Susceptible-Infected-Recovered (SIR) models are used in epidemiology to determine the spread of disease. (link) The Bass models for new product diffusion are textbook in sales. (link) ...
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1answer
62 views

Beta distribution vs beta binomial distribution: alpha and beta

I have been attempting to estimate alpha and beta from a beta binomial distribution given my data. There are R packages like VGAM to do this. I am wondering if there is a difference between estimating ...
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2answers
67 views

How do you count the number of parameters in a time series model?

I am learning about time series analysis and want to perform Box-Ljung tests of the residuals of my fitted models, e.g. ...
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13 views

Does Prism use smoothing to calculate a non-linear fit to data?

I have some read out vs. concentration of an agonist. I calculated EC50 using Prism6. My method was pretty simple. Log transform concetrations. Fit the data using log(agonist) vs. response -- ...
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1answer
16 views

Is golden section search considered a fitting (regression analysis)?

I am curious if the Golden section search is a form of fitting (or regression analysis in general)? It does find the extremum, but independent of any functional form (it works without modeling, if I ...
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24 views

Why does Empirical Bayes work in my simple case?

I have a problem where I am trying to classify data into two groups using a single parameter. The distribution of this parameter is Gaussian for two groups, so what I'm dealing with is two overlapping ...
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41 views

What have I done wrong implementing this Bayesian method for fitting a circle to noisy data?

I have noisy measurements of movement along a circle. I want to fit a circle to these measurements. I tried two methods, a straight forward moment fit, and then an ODR fit (described here. However ...
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31 views

How can I fix a poor nonlinear curve fit?

I was trying calculating Fourier transform of some rings. as follow: By directly calculating of model as several rings, the result showed different from the the experimental ones. So I tried to ...
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1answer
54 views

Find distribution of underlying feature

Let's say I have a dataset with values for the variable $W$. The distribution of $W$ doesn't follow any obvious known distribution. I have a model that gives $W$ as a functions of $E$ and $K, W = ...
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2answers
92 views

Fitting a GEV distribution - non-negative only

I am fitting a GEV distribution to some rainfall data, but the software I am using (Matlab and Easyfit) are giving a distribution which includes negative numbers (i.e. negative rainfall). Is there a ...
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24 views

estimating model fit parameters using simulations

I'm trying to fit 2D ellipticals gaussians to an image (with correlated background noise) using prewritten fitting software. I'd like to know about the uncertainty in the fit parameters with this ...
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35 views

loglikelihood for HMM with continuous emissions

I have a HMM and that has continuous valued emissions. I model the emissions using Weibull distributions. After I run the HMM I get the states, transition probabilities, priors and shape,scale ...
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7 views

Fit vertices to minimize Error when linearly interpolating

For a curve like the one below: Given that we have a certain amount of vertices for approximation, say 5. How to find appropriate x values to place the vetices on ...
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37 views

Fitting multiple normal distributions to sample data

I have a data set of (time, action)-tuples. Actions are typically performed at approximately the same times every day, and depending on what the action is it may be done multiple times per day. If I ...
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1answer
109 views

Fitted Beta distribution always holds water. Can I force it not to?

I am trying to fit a beta distribution to election forecast data. The ultimate purpose is determining with what probability the election will be decided by one vote (more on this here). My data is as ...
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0answers
28 views

geeglm not recognizing clusters

I am fitting a geeglm model and it is not recognizing the clustering. my model is ...
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142 views

How to determine if GLM quadratic term should be set up orthogonal or non-orthogonal

I am setting up a GLM in R where I have only one predictor variable and its quadratic form. I understand that in R I have 2 options. ...
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40 views

Do we fit this time series data with time series model or spline?

Basically, I have the following data with the number of item A on the vertical axis and the time on the horizontal axis (from 1st hour to the 24th hour). I don't have much experience in fitting a ...
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118 views

Align two datasets in Python

I want to develop some python code to align datasets obtained by different instruments recording the same event. As an example, say I have two sets of measurements: ...
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56 views

How do I verify whether a population distribution is a power-law? [duplicate]

given a population of discrete values (not a sample), is there any way to check whether the distribution is a power-law, and with what parameters? Of course I can just plot the distribution and see ...
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28 views

Least-squares fitting with only optimum features, after Lasso - valid?

Using Lasso reduces the coefficients of features of a model, reducing some to zero, and thereby performing feature selection. The number of features depends on the value of $\alpha$ aka $\lambda$. In ...
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22 views

Least Squares Regression - Error [duplicate]

In standard least squares regression, we find constants $\beta_1$ and $\beta_2$ such that the square of the average error, $\epsilon = y_i - (\beta_1 + \beta_2x_i)$, is minimized, and so the 'line of ...